The wealthy co-founder of LinkedIn has reportedly offered to donate $5m (£3.75m) to US military veterans if Republican presidential candidate Donald Trump reveals his tax affairs before the final debate of the election.

Historically it has been traditional for presidential nominees to bare their returns during a campaign, but Trump has so far refused to do so, claiming he will not release the returns until after the Internal Revenue Service completes its audit of his taxes.

There's no legal impediment to Trump revealing the figures before an audit is complete. Critics believe Trump is holding back because his income is less than he has boasted or the taxes he is paying are so low it will anger his constituency.

"In a functioning democracy, the public shouldn't be forced to bargain with a major presidential candidate to obtain access to his tax returns," LinkedIn chairman Reid Hoffman wrote in a post on Medium.

"And for the last 40 years, it hasn't had to. With the exception of Gerald Ford, every major candidate has shared this information with voters." Hillary Clinton released eight years of tax returns in 2015. She released her 2015 returns in August 2016.

Hoffman was moved to take action by a crowdfunding Internet appeal by US Marine veteran Pete Kiernan, who vowed to donate money he raised for nonprofit veterans group if Trump releases his returns by 19 October, 2016, the date of the final presidential debate.

Hoffman said if Kiernan meets his target, he will match whatever he raises up to five times, estimated around $5m (£3.75m).

Ironically, Trump offered the same amount to a charity of Barack Obama's choice in 2012 if the president would release his college records and applications, and his "passport applications and records." At the time Trump called Obama the "least transparent president in history."

In 2011 Trump told ABC News "maybe" he would release his tax returns if he ran for president in 2012 if Obama would release his birth certificate; Trump has supported so-called "birthers" who do not believe Obama was born in the US, but in Africa, even though the state of Hawaii has released Obama's birth certificate.

Trump's tax records have become the holy grail of the campaign. Dean Baquet, editor in chief at the New York Times, said he'd publish a story on Trump's taxes even if it meant risking jail time. He made the remark at a Harvard University forum when he was asked about the legal risks tied to publishing a leaked or hacked copy of Trump's taxes, CNN reported.

Baquet said Trump's taxes are important because he is "a presidential candidate whose whole campaign is built on his success as a business man, and his wealth," and his taxes could cast light on whether that's true.

"I think every journalist on the planet wants Donald Trump's tax returns," said Laura Poitras, the Academy Award-winning filmmaker who made a documentary about US National Security Agency leaker Edward Snowden.

Reid Hoffman is among a long parade of Silicon Valley heavy hitters who have criticised Trump. Facebook board member Peter Thiel is one of the few tech notables to have publicly supported Trump.

In July of this year, more than 100 technology sector leaders signed a letter calling Trump a "disaster for innovation." Just days ago, Facebook Inc. co-founder, Dustin Moskovitz, said he would commit $20m (£15m) to help Democrats in the election, including Hillary Clinton.